Thanks everybody for the input.
Everything is already built so the question was whenever by soldering some jumper wires, capacitors, diodes, etc. between these two boards can make them sync somehow. If it is not possible, I'll use some microcontroller, with phased PWM output, dead times, etc - I have done all that before, so no issue with that, except that requires compete disassembly of already built device.
I already tried reducing the frequency of one of 555, but flicker is really still there, unless I make it something like 2khz instead of 20khz. But, 2khz causes flicker issues when camera shutter is set to high speed. I have not tried to run say one 555 at 20khz and another one at 40khz, should this work?